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प्रश्न
Prove the following identity :
`(1 - tanA)^2 + (1 + tanA)^2 = 2sec^2A`
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उत्तर
LHS = `(1 - tanA)^2 + (1 + tanA)^2`
= `1 + tan^2A - 2tanA + 1 + tan^2A + 2tanA`
= `2(1 + tan^2A) = 2sec^2A` = RHS
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संबंधित प्रश्न
Prove the following trigonometric identities.
`(cos theta - sin theta + 1)/(cos theta + sin theta - 1) = cosec theta + cot theta`
Prove the following trigonometric identities.
`(1/(sec^2 theta - cos theta) + 1/(cosec^2 theta - sin^2 theta)) sin^2 theta cos^2 theta = (1 - sin^2 theta cos^2 theta)/(2 + sin^2 theta + cos^2 theta)`
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec theta)`
`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`
Prove the following identity :
secA(1 + sinA)(secA - tanA) = 1
Prove the following identity :
`sin^4A + cos^4A = 1 - 2sin^2Acos^2A`
To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.
Activity:
L.H.S. = `square`
= `square/(sinθ) + (sinθ)/(cosθ)`
= `(cos^2θ + sin^2θ)/square`
= `1/(sinθ.cosθ)` ...`[cos^2θ + sin^2θ = square]`
= `1/(sinθ) xx 1/square`
= `square`
= R.H.S.
Prove that `sqrt(sec^2 theta + "cosec"^2 theta) = tan theta + cot theta`
